IDEFIX

IDEFIX - 2025

2025Activity reportProject-TeamIDEFIX‌

RNSR: 202124274Y

Research center Inria Saclay Centre at‌ Institut Polytechnique de Paris
In partnership with:EDF‌ R&D, Ecole nationale supérieure des techniques avancées -‌ Institut polytechnique de Paris
Team name: Inversion of‌ Differential Equations For Imaging and physiX

Creation of‌ the Project-Team: 2021 August 01

Each year, Inria‌ research teams publish an Activity Report presenting their‌ work and results over the reporting period. These‌ reports follow a common structure, with some optional‌ sections depending on the specific team. They typically‌ begin by outlining the overall objectives and research‌ programme, including the main research themes, goals, and‌ methodological approaches. They also describe the application domains‌ targeted by the team, highlighting the scientific or‌ societal contexts in which their work is situated.‌

The reports then present the highlights of the‌ year, covering major scientific achievements, software developments, or‌ teaching contributions. When relevant, they include sections on‌ software, platforms, and open data, detailing the tools‌ developed and how they are shared. A substantial‌ part is dedicated to new results, where scientific‌ contributions are described in detail, often with subsections‌ specifying participants and associated keywords.

Finally, the Activity‌ Report addresses funding, contracts, partnerships, and collaborations at‌ various levels, from industrial agreements to international cooperations.‌ It also covers dissemination and teaching activities, such‌ as participation in scientific events, outreach, and supervision.‌ The document concludes with a presentation of scientific‌ production, including major publications and those produced during‌ the year.

Keywords

Computer Science and Digital Science‌

A6.1. Methods in mathematical modeling
A6.1.1. Continuous Modeling‌ (PDE, ODE)
A6.1.4. Multiscale modeling
A6.2.1. Numerical analysis‌ of PDE and ODE
A6.2.6. Optimization
A6.2.7. HPC‌ for machine learning
A6.3.1. Inverse problems
A6.5.4. Waves‌
A9.2. Machine learning

1 Team members, visitors, external‌ collaborators

Research Scientists

Lorenzo Audibert [Team leader‌, EDF]
Houssem Haddar [Team leader‌, INRIA, Senior Researcher, HDR]‌
Marcella Bonazzoli [INRIA, Researcher]
Lucas‌ Chesnel [INRIA, Researcher]
Jing-Rebecca Li-Schlittgen‌ [INRIA, Senior Researcher, HDR]‌
Hadrien Montanelli [INRIA, Researcher]

Faculty‌ Members

Elise Grosjean [ENSTA, Associate Professor‌]
Zoïs Moitier [ENSTA, Associate Professor‌]

Post-Doctoral Fellows

Duc Quang Bui [INRIA‌, Post-Doctoral Fellow, until Jun 2025]‌
Michele Zaccaron [ENSTA, Post-Doctoral Fellow,‌ from Sep 2025]

PhD Students

Mayeul Chavanne‌ [INRIA]
Victor Chenu [INRIA]‌
Corentin Hivart [EDF, CIFRE]
Esteban Jung‌ [ENSTA, from Oct 2025]
Morgane‌ Mathevet [EDF, CIFRE, until Sep 2025]
Alex Mc‌ Sweeney-Davis [EDF,‌ CIFRE]

Technical Staff‌‌

Sara Sedlar [INRIA, Engineer, until‌ Nov 2025]

Interns‌ and Apprentices

Emna Abida‌‌ [INRIA, Intern, from Apr 2025‌ until Sep 2025]‌
Aatae Boulette [INRIA‌‌, Intern, from May 2025 until Aug‌ 2025]
Thomas Creuset‌ [INRIA, Intern‌‌, from May 2025 until Aug 2025]‌
Abdallah Mrabti [INRIA‌, Intern, from‌‌ Jun 2025 until Sep 2025]
Anis Oueslati‌ [INRIA, Intern‌, from Jul 2025‌‌ until Sep 2025]

Administrative Assistant

Marie Enee‌ [INRIA]

Visiting‌ Scientists

Slim Chaabane [‌‌FSS]
Noureddine Mhamdi [IPEIK, from‌ Jun 2025 until Jul‌ 2025]
Chaima Regaieg‌‌ [IPEIS, from Jun 2025 until Jul‌ 2025]

External Collaborators‌

Didier Boldo [EDF‌‌]
Guy D'Urso [EDF]
Alexandre Girard‌ [EDF]
Jean-Marie‌ Henault [EDF]‌‌
Morgane Mathevet [INRIA, from Sep 2025‌ until Oct 2025]‌
Frederic Taillarde [EDF‌‌, HDR]
Denis Vautrin [EDF]‌

2 Overall objectives

Inverse‌ problems are encountered in‌‌ many real life applications and the ones we‌ are interested in are‌ those that can be‌‌ formulated as parameter identifications in a PDE (system)‌ modeling physical phenomena, primarily‌ wave propagation and diffusion.‌‌ As opposed to determining the solution of the‌ forward model, identifying the‌ parameters from measurements of‌‌ this solution usually leads to an unstable and‌ non linear problem that‌ may be not uniquely‌‌ solvable. A standard method to formulate this inverse‌ problem is to consider‌ it as a minimization‌‌ of a cost functional that measures data fidelity.‌ The solution to the‌ latter is computationally much‌‌ more costly than solving the PDE and may‌ even not be realistic‌ for number of applications‌‌ that require real time answers or for very‌ large scale problems. These‌ considerations motivated the research‌‌ guidelines items exposed above and that we shall‌ develop further in the‌ following.

At EDF, the‌‌ need for algorithms to solve inverse problems is‌ present in numerous applications‌ (see Section 4 for‌‌ instance). The team Signal, Image and Learning at‌ EDF R&D, PRISME has‌ developed solutions mainly based‌‌ on signal processing methods that do not require‌ fine modeling of the‌ physical phenomena (describing the‌‌ experiment). This enables fast simplified responses that can‌ usually be satisfactory. The‌ complexification of the measuring‌‌ devices and environments appealed for more precise assessment‌ of the experiments and‌ therefore for more reliable/precise‌‌ inversion methods. This was the motivation behind the‌ intense collaborations between EDF‌ R&D and the DEFI‌‌ project team that lead to six co-supervised PhD‌ thesis and one PostDoc‌ on various themes (Eddy‌‌ current imaging for pipes, data assimilation for primary‌ cooling loops, sampling methods‌ for concrete like materials,‌‌ multi-element eddy current 3-D probes, qualitative inversion methods‌ and spectral signatures for‌ ultrasound applications). The joint‌‌ team aims at pursuing‌ this collaborative effort that has been beneficial to‌ both partners, motivating at the same time fundamental‌ research to establish solid theoretical foundations of promising‌ inversion methods and (non trivial) adaptations of established‌ methods to solve applications of interest for EDF.‌

3 Research program

Let us describe the outline‌ of the main challenges that we would like‌ to address for solutions to inverse problems, taking‌ as a guideline the example of non destructive‌ testing which is central for EDF applications. A‌ typical experiment would be to probe some defects‌ inside a given structure by sending waves that‌ can propagate inside the domain of interest. The‌ response of the media is recorded by some‌ receivers and forms the data of the inverse‌ problem. We can distinguish two types of inverse‌ problems. In the first type, referred to by‌ “imaging”, one is interested by only the location‌ and/or the shape of the defect/inclusion. In the‌ second one, referred to by “identification”, one is‌ interested in getting information on the defect physical‌ properties. Both problems (imaging and identification) are non‌ linear and ill-posed (lack of stability with respect‌ to measurements errors if some careful constrains are‌ not added). Moreover, the unique determination of the‌ geometry and/or the coefficients is not guaranteed in‌ general if sufficient measurements are not available. As‌ an example, in the case of anisotropic inclusions,‌ one can show that an appropriate set of‌ data uniquely determine the geometry but not the‌ material properties. These theoretical considerations are usually difficult‌ to address and are not only important in‌ understanding the mathematical properties of the inverse problem,‌ but also guide the choice of appropriate numerical‌ strategies (which information can be stably reconstructed) and‌ also the design of appropriate regularization techniques and‌ improve the measurement techniques. Moreover, uniqueness proofs can‌ be constructive proofs, i.e. they implicitly contain a‌ numerical algorithm to solve the inverse problem, hence‌ their importance for practical applications. The sampling methods‌ introduced below are one example of such algorithms.‌ As a complementary notion to identifiability is the‌ notion of invisibility. The latter topic has attracted‌ a large attention in the inverse problem community‌ due in particular to the recent and rapid‌ development of metamaterials that made plausible the design‌ of cloaking devices based on transformation optics. However,‌ these transformations require the use of non dissipative‌ materials exhibiting singular physical coefficients taking infinite values,‌ which is indeed not realistic. This motivated us‌ to consider a weaker notion of invisibility where‌ one would like to achieve invisibility for only‌ a finite set of measurements and frequencies. This‌ objective is less ambitious and consequently, it is‌ more easily achievable. On the other hand, it‌ is pertinent from a practical point of view‌ because one always has a finite number of‌ sensors and very often, one has only access‌ to a small number of measurements. In addition‌ to theoretically investigate this issue for some idealized models, we would like‌ to fructify our findings‌ for non destructive testings‌‌ in waveguides.

An important part of our research‌ activity is dedicated to‌ numerical methods applied to‌‌ the first type of inverse problems, where only‌ the geometrical information is‌ sought. In its general‌‌ setting the inverse problem is very challenging and‌ no method can provide‌ a universal satisfactory solution‌‌ to it (regarding the balance cost-precision-stability). This is‌ why in the majority‌ of the practically employed‌‌ algorithms, some simplification of the underlying mathematical model‌ is used, according to‌ the specific configuration of‌‌ the imaging experiment. The most popular ones are‌ geometric optics (the Kirchhoff‌ approximation) for high frequencies‌‌ and weak scattering (the Born approximation) for small‌ contrasts or small obstacles.‌ They actually give full‌‌ satisfaction for a wide range of applications as‌ attested by the large‌ success of existing imaging‌‌ devices (radar, sonar, ultrasound, X-ray tomography, etc.), that‌ rely on one of‌ these approximations.

Generally speaking,‌‌ the used simplifications result in a linearization of‌ the inverse problem and‌ therefore are usually valid‌‌ only if the latter is weakly non-linear. The‌ development of these simplified‌ models and the improvement‌‌ of their efficiency is still a very active‌ research area. With that‌ perspective we are particularly‌‌ interested in deriving and studying higher order asymptotic‌ models associated with small‌ geometrical parameters such as‌‌ small obstacles, thin coatings, periodic media, $...$ .‌ Higher order models usually‌ introduce some non linearity‌‌ in the inverse problem, but are in principle‌ easier to handle from‌ the numerical point of‌‌ view than in the case of the exact‌ model. Asymptotic analysis is‌ also a corner stone‌‌ in our methodology to prove invisibility for finite‌ number of measurements.

A‌ major research axis is‌‌ dedicated to algorithms that avoid the use of‌ such approximations and that‌ are efficient where classical‌‌ approaches may fail: i.e. roughly speaking when the‌ non linearity of the‌ inverse problem is sufficiently‌‌ strong. This type of configuration is motivated by‌ the applications mentioned below,‌ and occurs as soon‌‌ as the geometry of the unknown media generates‌ non negligible multiple scattering‌ effects (multiply-connected and closely‌‌ spaces obstacles) or when the used frequency is‌ in the so-called resonant‌ region (wave-length comparable to‌‌ the size of the sought medium). It is‌ therefore much more difficult‌ to deal with and‌‌ requires different approaches such as sampling methods. The‌ sampling methods are fast‌ imaging solvers adapted to‌‌ multi-static data (multiple receiver-transmitter pairs). Even if they‌ do not use any‌ linearization of the forward‌‌ model, they rely on computing the solutions to‌ a set of linear‌ problems of small size,‌‌ that can be performed in a completely parallel‌ procedure. Our team is‌ among the leading international‌‌ groups in the developments of these techniques. We‌ are one of the‌ main contributors in recent‌‌ advancements in this field and actively acting in‌ its dissemination among the‌ academic and industrial communities.‌‌ We shall pursue our‌ efforts in developing and promoting these techniques. A‌ closely related subject is the study of so-called‌ Transmission eigenvalues that naturally arise in the analysis‌ of inverse medium problems and particularly in the‌ theory behind sampling methods. These frequencies can be‌ seen as the extension of the notion of‌ resonant frequencies for impenetrable objects to the case‌ of penetrable media. Our developments of sampling methods‌ lead us to discover that transmission eigenvalues can‌ be reconstructed from multi-frequency and multistatic measurements. The‌ spectrum formed by these special frequencies can be‌ related to the materiel properties of the medium‌ and therefore can be used as a signature‌ that characterizes some aspects of this medium (although‌ a complete answer to this statement is far‌ from being available). More specifically we promote the‌ use of these quantities to obtain qualitative information‌ on changes in the probed domain (as in‌ non destructive testing). The study of transmission eigenvalues‌ has become (as for sampling methods) a well‌ identified branch in the inverse problem community that‌ raises many challenges ranging from purely theoretical questions‌ to numerical schemes and significance for applications.

For‌ the identification problem, one would also like to‌ have information on the physical properties of the‌ targets. Of course optimization methods is a tool‌ of choice for these problems. The application of‌ non linear optimization methods for inverse problems has‌ to be supplemented by regularization strategies. While convergence‌ for Hilbertian regularization is well understood from the‌ theoretical point of view, it is still far‌ from being the case for non Hilbertian norms.‌ For instance regularization strategies that promote sparsity belong‌ to the latter class and is of great‌ interest for inverse problems where the coefficients have‌ singularities (point sources, crack like defects, piecewise constant‌ material properties, etc...). Exploring theoretical and numerical issues‌ raised by these regularization is of interest for‌ applications. We plan to invest on these issues‌ together with the use of non standard fidelity‌ functional that may help reducing the number of‌ local minima. Combining deterministic techniques with stochastic ones‌ is also an interesting perspective that has not‌ been sufficiently explored in the literature and that‌ we aim at developing. This would allows us‌ to also investigate feasibility of Bayesian inference for‌ these non linear and computationally involving inverse problems.‌ Exploiting neural networks in the design of solutions‌ to inverse problems is major trend in the‌ inverse problem community as in many other scientific‌ area. Using these techniques to directly solve severe‌ ill posed problems, as inverse scattering problems, does‌ not seem a certifiable route. A more reasonable‌ approach to benefit from the ability of these‌ networks to encode high dimensional complex non linear‌ functional would be to use them for automatically‌ adjusting deterministic optimization parameters such as descent steps‌ and/or regularization parameters (or priors). This also holds‌ true for their use in the sampling methods‌ invoked above and we shall start by exploring this combination first.

From‌ the practical point of‌ view, the major limitation‌‌ of sampling methods would be the need of‌ a large amount of‌ data to achieve a‌‌ reasonable accuracy. On the other hand, optimization methods‌ do not suffer from‌ this constrain but they‌‌ require good initial guess to ensure convergence and‌ reduce the number of‌ iterations. Therefore it seems‌‌ natural to try to combine the two class‌ of methods in order‌ to calibrate the balance‌‌ between cost and precision.

Independently from the formulation‌ of the optimization problem,‌ the efficiency of inversion‌‌ algorithm associated with this formulation greatly depends on‌ the efficiency of the‌ forward solver. Our team‌‌ has already made significant contributions in acceleration techniques‌ for solutions to the‌ forward problem (waves and‌‌ diffusion). We developed strong expertise in H-matrix compression‌ and combination with other‌ acceleration techniques such as‌‌ FFT and fast multipole methods for wave problems.‌ Fructifying this into the‌ solution to large scale‌‌ inverse problems in link with geophysical application or‌ non destructive testing is‌ promising for obtaining feasible‌‌ inversion algorithm for the full non linear inverse‌ problem. Domain decomposition technique‌ is yet another expertise‌‌ that we have developed and would like to‌ explore for accelerating the‌ solution of the forward‌‌ and inverse problems. For the latter, methodologies where‌ iterations on the inversion‌ parameter and the forward‌‌ and adjoint problems are combined merit investigations. Several‌ approaches have been proposed‌ in the literature, but‌‌ the convergence of these schemes and their efficiency‌ are not yet clear‌ in the context of‌‌ inverse ill-posed problems.

Although a major focus will‌ be given to applications‌ and methodologies that can‌‌ be of interest for EDF, the contours of‌ the IDEFIX research team‌ include topics that may‌‌ go beyond that perspective.

In particular we are‌ also interested in applications‌ involving the imaging of‌‌ biological tissues with the technique of Diffusion Magnetic‌ Resonance Imaging (DMRI). Roughly‌ speaking, DMRI gives a‌‌ measure of the average distance travelled by water‌ molecules in the imaged‌ medium and can give‌‌ useful information on cellular structure and structural change‌ when the medium is‌ biological tissue. In particular,‌‌ we would like to infer from DMRI measurements‌ changes in tissue and‌ cellular structure occurring under‌‌ various physiological or pathological conditions, as well generally‌ the cell morphology in‌ the region of interest.‌‌ The main challenges here are: 1) to model‌ correctly the measured signals‌ using diffusive-type evolution equations,‌‌ 2) to handle numerically the geometical complexity of‌ biological issue; 3) to‌ use the first two‌‌ to identify physically relevant parameters from the measurements.‌ There are two main‌ groups of approaches to‌‌ the first two challenges. The first one relies‌ on using random walkers‌ to mimic the diffusion‌‌ process in a given geometrical configuration. The second‌ one exploits the model‌ given by the Bloch-Torrey‌‌ partial differential equation, which describes the evolution of‌ the complex transverse water‌ proton magnetization under the‌‌ influence of diffusion-encoding magnetic‌ field gradients pulses. We primarily work in the‌ simulation and analysis of the Bloch-Torrey partial differential‌ equation in complex geometries, in other words, we‌ follow the second group of approaches. For the‌ third challenge, we are particularly interested in constructing‌ reduced models of the multiple-compartment Bloch-Torrey model using‌ homogenization methods. To solve difficult problems in diffusion‌ MRI on realistic cellular geometries, we use a‌ variety of approaches including finite elements discretization, Laplace‌ eigenfunctions, and machine learning, coupled with advanced techniques‌ such as HPC, low rank approximations, and layer‌ potential representations.

4 Application domains

4.1 Eddy Current‌ Imaging for steam generator and rotating machine

Eddy‌ Current is an approximation of Maxwell system at‌ low frequency. Probe that works in that quasi-stationary‌ regime are commonly used in non destructive testing.‌ We are interested in inverse problems for these‌ type of measurement in steam generator and more‌ recently for rotating machine.

Steam generators are critical‌ components in nuclear power plants. For a sake‌ of radioactive safety, the water flow (called the‌ primary fluid) which ensures the cooling of the‌ core reactor is separated from the water flow‌ (called the secondary fluid) which is transformed in‌ steam to generate electricity: the heat must be‌ transferred via the steam generator. The primary fluid‌ circulates in tubes with U-shape while the secondary‌ fluid rises up in the steam generator along‌ these tubes.

Without disassembling the steam generator, the‌ lower part of the U-tubes is inaccessible for‌ normal inspections. Therefore, a non-destructive examination procedure, called‌ eddy current testing (ECT), is usually used to‌ detect the presence of deposits. In an ECT,‌ one introduces a probe consisting of coils of‌ wire in the tube that deliver electromagnetic excitation‌ at low frequencies (eddy current regime) and measure‌ induced currents by the external media (ECT signals).‌ The design of robust and reliable PDE based‌ inversion methods to analyze ECT signals is a‌ long term ongoing project with and within EDF‌ R&D. We first developed and analyzed the simplified‌ setting of axisymmetric geometries which allows to model‌ the problem in 2D and to test various‌ options for the direct and inverse algorithms and‌ in particular an algorithm based on the Level‌ Set method. We start extending this work to‌ 3D inversions for various types of probes (with‌ angular resolutions) and various types of defects. And‌ will pursue this in the future in order‌ to treat real data with multiple defects (i.e.‌ cracks, deposit, thin deposit).

Finally related to Eddy‌ Current modeling, we work on low frequency/quasi-stationary Maxwell‌ system in alternators and engines. On those systems‌ EDF is trying to assess from measurements the‌ exact geometry and the physical properties which have‌ potentially (parametric) non linear constitutive laws. A collaboration‌ on this topic with the EDF team that‌ contributes to code CARMEL. Together with the same‌ team and others, we submit a project on‌ an experimental facilities for eddy current where we will contribute on the‌ calibration of the data‌ using inverse problems methodology‌‌ and extension to geometry not limited to pipes.‌

4.2 Non destructive testing‌ of concrete-like material

Concrete‌‌ is a widely used material thanks to its‌ appealing (when reinforced) properties‌ and its manageable cost.‌‌ However, it is a very complex material: highly‌ heterogeneous, multiscale, evolving over‌ time, etc. Yet, it‌‌ has to be inspected to ensure that the‌ structure is safe and‌ especially when this structure‌‌ is part of sensitive infrastructures such as power‌ plants. Using mechanical waves‌ to inspect concrete is‌‌ widely used in practice but many aspects still‌ constitute very challenging problems‌ due to the complex‌‌ properties of the material. Several defects are of‌ interest and measurements might‌ vary with respect to‌‌ the target. Imaging are very difficult with conventional‌ techniques due to potentially‌ low contrast and complicated‌‌ structure (i.e. reinforcing bar, metallic liners). Sampling methods‌ are able to tackle‌ this type of problem‌‌ by integrating the information on the a priori‌ structure of the geometry.‌ Other methods such as‌‌ homogenization could be a valuable approached for identifying‌ this type of defects.‌

The region between air‌‌ and the first reinforcement steel bar are of‌ primary importance because it‌ shields the steel from‌‌ the exterior and therefore prevents corrosion. To inspect‌ this area, engineers rely‌ on surface wave techniques‌‌ similar to Multi-channel Analysis of Surface Waves (MASW)‌ in geophysics. However, concrete‌ is not a layered‌‌ material and therefore interpretation of this type of‌ measurements is not easy.‌ Basically this method constructs‌‌ the dispersion curve of surface waves through data‌ processing and then uses‌ this information to invert‌‌ a layered model for the material. This procedure‌ shares similarities with spectral‌ signature identification and it‌‌ would be interesting to further clarify this link‌ in order to obtain‌ better interpretation (or reformulation)‌‌ of MASW in this context.

Similarly to ultrasonic‌ waves, electromagnetic waves are‌ generally used to inspect‌‌ concrete type materials, we will be involved in‌ imaging complex structure with‌ radar type measurements. A‌‌ more challenging application is to determine the electromagnetic‌ properties of the material‌ and relate them to‌‌ the hydration of the cement paste. MASW analysis‌ of the measurements are‌ also consider in this‌‌ setting similarly to mechanical waves.

4.3 Subsurface imaging‌

Subsurface imaging up to‌ one hundred meters is‌‌ of primary importance for power plant safety assessment‌ with respect to seismic‌ activity. Issues range from‌‌ testing the interface between the bedrock and the‌ bottom of dam, to‌ quantitative map and detection‌‌ of fracture underneath nuclear power plant and imaging‌ of the sea bed‌ to evaluate the feasibility‌‌ of construction of offshore wind turbine. Earth imaging‌ is a well studies‌ area but primarily at‌‌ medium to long distance thanks to oil industry‌ and seismology. However subsurface‌ imaging is not very‌‌ common and has its own difficulties due to‌ the heterogeneous structure of‌ the soil and the‌‌ higher frequency of the‌ wave needed to have a satisfactory resolution.

Dykes‌ are structures that are difficult to inspect but‌ are of primary importance for the safety of‌ power plant and MASW is usually applied for‌ that purpose. Using data processing techniques dispersion curves‌ are extracted from recorded surface waves. Engineers then‌ use semi-analytic model of dispersion curves for stratified‌ media to obtain an subsurface image. Extending this‌ type of methods to non-stratified media is challenging‌ and it would be interesting to see how‌ it compares with classical optimization based inversion methods.‌

As for concrete imaging mechanical, electromagnetic waves and‌ conductivity are the various physics used to probe‌ the medium. Both shared heterogeneous physical properties, embedded‌ in potentially complex geometries and seek unknown of‌ several types and are applications less investigated that‌ medical, seismic or metallic imaging. As research on‌ measurements techniques are carried by the same group‌ in EDF R&D PRISME we will seek for‌ synergy between this two fields.

4.4 Applications of‌ concepts related to invisibility for finite set of‌ measurements

As mentioned above, in the team we‌ have developed different approaches to construct obstacles which‌ are invisible for imaging techniques with a finite‌ number of measurements. In what we did, obstacles‌ are invisible at a fixed frequency. It would‌ be important to study more the sensitivity of‌ the invisibility results with respect to the frequency.‌ In the construction algorithms, can we add constraints‌ so that invisibility remains robust to the frequency?‌ In our studies, we have mainly focused our‌ attention on acoustics in waveguides. It would be‌ interesting to investigate electromagnetic and elasticity problems. Moreover,‌ it would be very instructive to investigate how‌ the invisible objects we design theoretically and numerically‌ behave in practice. To proceed, we contemplate to‌ work with experimentalists at the Acoustic Department of‌ the University of Le Mans with whom we‌ are in contact.

Until now, we have only‌ constructed obstacles which are invisible in time-harmonic regime.‌ It would be interesting to study what can‌ be done for time dependent problems. Maybe the‌ first question is as follows: imagine that a‌ time dependent source term is given (a pulse),‌ how to design the geometry so that the‌ signal passes through the structure as if they‌ were no defect? For the applications, one can‌ think to the optimal design of a stent‌ to fix a damaged coronary artery. It is‌ known that an inappropriate shape and material for‌ the stent can produce scattered waves which are‌ harmful for the cardiac muscle.

In the physical‌ community, spectacular advances have recently been made in‌ the development of a new field called “wave‌ front shaping” . For a given unknown complex‌ scatterer, the goal is to find the best‌ entrance signal to obtain a given physical property‌ (focalisation of the energy, good transmission, ...). We‌ emphasize that in this context, optimization techniques cannot‌ be used because the scatterer is complex and a priori unknown. This‌ point of view is‌ different from the one‌‌ considered up to know in the team. Indeed,‌ in our case, the‌ entrance signal is given‌‌ and we look for the scatterer to have‌ invisibility. It would be‌ interesting to study the‌‌ connections existing between the two approaches.

Another area‌ which would benefit from‌ the expertise of the‌‌ team is the design of barriers that would‌ isolate critical buildings of‌ nuclear power plant from‌‌ seismic solicitation. This topic is directly related to‌ the partial invisibility exposed‌ above. Indeed, for this‌‌ application, complete cloaking is not necessary as it‌ is enough to transfer‌ the seismic solicitation to‌‌ other area in space and to reduce the‌ maximal solicitation on specific‌ modes of the structure‌‌ (either by spreading the solicitation in time or‌ by transferring the solicitation‌ to a more robust‌‌ mode of vibration). This boils down to design‌ structures ensuring zero transmission‌ of energy between different‌‌ given modes, a question we also consider in‌ our works dealing with‌ waves propagation in waveguides.‌‌ This problematic has not yet been planned by‌ EDF in the short‌ term perspectives but we‌‌ believe it is worth exploring as there already‌ exist realistic experiments of‌ such cloaking constructions formed‌‌ by stilts embedded in the soil.

4.5 Other‌ potential applications of interest‌ for EDF

One way‌‌ to measure flow rate in stationary environment is‌ to use ultrasound measurements.‌ Ultrasound propagates faster in‌‌ the direction of the flow and slower in‌ the opposite direction. This‌ principle has been used‌‌ to measure flow rate in pipes with relatively‌ clear water. It is‌ also used for water‌‌ carrying heterogeneities, like bubbles, sand, stone... but with‌ an experimental approach, with‌ few understanding of the‌‌ limits of the method. Being able to model‌ the propagation in such‌ an heterogeneous medium and‌‌ to adapt the analysis of the data would‌ not only improve current‌ measurement techniques but also‌‌ give tools to know a priori the method‌ limits. There are issue‌ in hydraulic power plants‌‌ to assess the presence of obstacles or objects‌ in moving fluid using‌ SONAR type measurements. Depending‌‌ on the application it is not clear yet‌ if the fluid motion‌ could be neglect and‌‌ it will be the purpose of further research.‌ These applications would be‌ a promising first step‌‌ to open our expertise towards fluid related problems,‌ which might have large‌ perspectives in our collaboration‌‌ with EDF. Similarly to non destructive testing of‌ concrete, other approaches rely‌ on electromagnetic or passive‌‌ measurements (sources of sound locations) in order to‌ assess the flow rate.‌

4.6 Diffusion MRI

The‌‌ diffusion magnetic resonance imaging signal arising from biological‌ tissues can be numerically‌ simulated by solving the‌‌ Bloch–Torrey partial differential equation. Numerical simulations can facilitate‌ the investigation of the‌ relationship between the diffusion‌‌ MRI signals and cellular structures. With the rapid‌ advance of available computing‌ power, the diffusion MRI‌‌ community has begun to‌ employ numerical simulations for model formulation and validation,‌ as well as for imaging sequence optimization. For‌ example, in collaboration with CHU de Rennes and‌ the EMPENN team at Inria Rennes, we aim‌ to develop a novel diffusion MRI sequence, optimized‌ towards clinical feasibility, that can contribute to defining‌ practically obtainable and robust imaging biomarkers of chronic‌ inflammation in patients with Multiple Sclerosis.

5 Latest‌ software developments, platforms, open data

5.1 Latest software‌ developments

5.1.1 ECIP

Name:
Eddy Current Imaging for‌ Pipes
Keywords:
Inverse problem, Partial differential equation, HPC,‌ Domain decomposition
Functional Description:
This software identifies deposit‌ on pipes from measurements of eddy current probes.‌ It is based on finite elements and domain‌ decomposition through the softwares HPDDM, PETSc and FreeFEM,‌ for the resolution of the PDE model of‌ the eddy current measurements. It uses an iterative‌ algorithm to identify the deposit properties.
Contact:
Lorenzo‌ Audibert
Partner:
Edf

5.1.2 SpinDoctor

Name:
SpinDoctor Diffusion‌ MRI Simulation Toolbox
Keywords:
MRI, Simulation, Finite element‌ modelling
Functional Description:

SpinDoctor can be used

1.‌ to solve the Bloch-Torrey PDE to obtain the‌ dMRI signal (the toolbox provides a way of‌ robustly fitting the dMRI signal to obtain the‌ fitted Apparent Diffusion Coefficient (ADC)), 2. to solve‌ the diffusion equation of the H-ADC model to‌ obtain the ADC, 3. a short-time approximation formula‌ for the ADC is also included in the‌ toolbox for comparison with the simulated ADC.
URL:‌
https://github.com/SpinDoctorMRI/
Contact:
Jing Rebecca Li

5.1.3 CASTOR

Keyword:‌
C++
Functional Description:

The objective of the castor‌ library is to propose high-level semantics, inspired by‌ the Matlab language, allowing fast software prototyping in‌ a low-level compiled language. It is nothing more‌ than a matrix management layer using the tools‌ of the standard C++ library, in different storage‌ formats (full, sparse and hierarchical). Indeed, the use‌ of IDEs 1 such as Xcode, Visual studio,‌ Eclipse, etc. allows today to execute compiled code‌ (C, C++, fortran, etc.) with the same flexibility‌ as interpreted languages (Matlab, Python, Julia, etc.).

A‌ header-only template library for matrix management has been‌ developed based on the standard C++ library, notably‌ the std::vector class. Many tools and algorithms are‌ provided to simplify the development of scientific computing‌ programs. Particular attention has been paid to semantics,‌ for a simplicity of use “à la matlab”,‌ but written in C++. This high-level semantic/low-level language‌ coupling makes it possible to gain efficiency in‌ the prototyping phase, while ensuring performance for applications.‌ In addition, direct access to data allows users‌ to optimize the most critical parts of their‌ code in native C++. Finally, complete documentation is‌ available, as well as continuous integration unit tests.‌ All of this makes it possible to meet‌ the needs of teaching, academic issues and industrial‌ applications at the same time.

The castor library‌ provides tools to :

create and manipulate dense,‌ sparse and hierarchical matrices make linear algebra computations‌ based on optimized BLAS library make graphical representations based on VTK library‌ These tools are used‌ by applicative projects :‌‌

finite and boundary element method using Galerkin approximation‌ analytical solutions for scattering‌ problems
URL:
https://leprojetcastor.gitlab.labos.polytechnique.fr/castor/#
Contact:‌‌
Matthieu Aussal

5.1.4 lostinmsh

Keywords:
Mathematics, Mesh generation‌
Functional Description:
The Python‌ toolbox lostinmsh (LOcally STructured‌‌ polygonal INterface MeSH), is a package using GMSH‌ to construct locally structured‌ triangular meshes of polygons‌‌ which are useful for sign changing PDE problem.‌
URL:
https://zmoitier.github.io/lostinmsh/
Contact:
Zois‌ Moitier

5.1.5 HAdaptiveIntegration.jl

Keywords:‌‌
Mathematics, Numerical analysis, Scientific computing
Functional Description:
Julia‌ package designed for numerical‌ integration over multidimensional domains.‌‌
URL:
https://zmoitier.github.io/HAdaptiveIntegration.jl/stable/
Contact:
Zois Moitier

5.1.6 Reduced Basis‌ Methods Documentation

Keywords:
Reduced‌ Basis Methods, Numerical simulations,‌‌ Finite element modelling
Functional Description:
This website provides‌ a basic introduction to‌ Reduced Basis Methods (RBM).‌‌ They aim at reducing the runtimes of classical‌ methods of resolution (e.g.‌ finite elements method) for‌‌ parameterized partial differential equations when they have to‌ be solved for many‌ different parameter values. They‌‌ have many applications arising from engineering and applied‌ sciences, such as real-time‌ simulation or calibration problems.‌‌ For each RBM (POD-Galerkin, PODI, NIRB two-grid, EIM,‌ PBDW), a short description‌ with links to several‌‌ articles is presented, and a simple application in‌ a Python notebook and‌ links to other computational‌‌ langages (such as Fenics/Feel++/FreeFem++) are provided.
Contact:
Elise‌ Grosjean

6 New results‌

6.1 Fast data driven‌‌ imaging methods

Participants: Lorenzo Audibert, Lucas Chesnel‌, Houssem Haddar,‌ Hadrien Montanelli, Jean-Marie‌‌ Henault.

6.1.1 Analysis of Sampling methods with‌ and without linearization

L.Audibert,‌ S. Meng

Sampling methods‌‌ were designed to identify the support of an‌ obstacle from multistatic measurements,‌ with theoretical guarantees that‌‌ do not rely on linearizing the scattering problem.‌ However, the indicator functions‌ they produce remain, to‌‌ some extent, poorly understood. In an initial study,‌ we derived computable quantities‌ that shed light on‌‌ the behavior of these indicator functions.

To push‌ this understanding further, we‌ turned to the Born‌‌ linearization, under which the Linear Sampling Method (LSM)‌ indicator can be interpreted‌ as a non-uniform average‌‌ of the reciprocal of the contrast. In doing‌ so, we uncovered for‌ the Born approximation an‌‌ unexpected and unphysical resampling and factorization of the‌ far-field operator, which enables‌ the combination of data‌‌ from multiple frequencies. This reformulation reduces the problem‌ to the analysis of‌ a restricted Fourier operator.‌‌

This operator naturally leads to the use of‌ Prolate Spheroidal Wave Functions‌ (PSWFs), well known in‌‌ harmonic analysis for their optimal concentration properties. We‌ then investigate the usefulness‌ of this basis for‌‌ linearized inverse scattering, assessing its potential for improved‌ reconstruction and understanding of‌ sampling-type indicators.

6.1.2 Fast‌‌ Imaging of Local Perturbations in a Unknown Bi-Periodic‌ Layered Medium

H. Haddar,‌ N. Jenhani

We consider‌‌ a nondestructive testing problem involving an infinite periodic‌ penetrable layer probed by‌ acoustic waves. This problem‌‌ is of growing interest, as periodic structures play‌ a central role in‌ many modern technological applications‌‌ across (bio)engineering and materials‌ science. In many advanced devices, however, the periodic‌ architecture may be highly complex or difficult to‌ model mathematically. As a result, evaluating its Green’s‌ function, an essential ingredient in numerous imaging techniques,‌ can become computationally expensive or even infeasible.

At‌ the same time, when analyzing flows or defects‌ in such complex media, fully reconstructing both the‌ periodic structure and the localized anomalies is often‌ unrealistic. In earlier work, we proposed an approach‌ that provides a criterion for identifying the support‌ of local anomalies without requiring explicit knowledge or‌ reconstruction of the healthy periodic background.

To address‌ more general scenarios related to this method, one‌ encounters the need to analyze an interior transmission‌ problem posed in an unbounded domain. This setting‌ renders classical approaches inapplicable, as the Rellich compactness‌ theorem cannot be used in unbounded geometries. In‌ 7, we introduced a new approach based‌ on the analysis of a semi-discretized reformulation of‌ the problem using the Floquet–Bloch transform.

6.2 Transmission‌ eigenvalues

Participants: Lorenzo Audibert, Lucas Chesnel,‌ Houssem Haddar.

6.2.1 Examples of non-scattering inhomogeneities‌

L. Chesnel, H. Haddar, H. Li, J. Xiao‌

We consider the scattering of waves by a‌ penetrable inclusion embedded in some reference medium. We‌ exhibit examples of materials and geometries for which‌ non-scattering frequencies exist, i.e., for which at some‌ frequencies there are incident fields which produce null‌ scattered fields outside of the inhomogeneity. We show‌ in particular that certain domains with corners or‌ even cusps can support non-scattering frequencies. We relate‌ the latter, for some inclusions, to resonance frequencies‌ for Dirichlet or Neumann cavities. We also find‌ situations where incident non-scattering fields solve the Helmholtz‌ equation in a neighbourhood of the inhomogeneity and‌ not in the whole space. In relation with‌ invisibility, we give examples of inclusions of anisotropic‌ materials which are non-scattering for all real frequencies.‌ We prove that corresponding material indices must have‌ a special structure on the boundary 4.‌

6.2.2 Averaged Steklov Eigenvalues, Inside OutsideDuality and Application‌ to Inverse Scattering

L. Audibert, Houssem Haddar and‌ Fabien Pourre

We introduce a new family of‌ artificial backgrounds corresponding to averaged impedance boundary conditions‌ formulated in an abstract framework. These backgrounds are‌ used to define a finite number of averaged‌ Steklov eigenvalues, which are associated with inverse scattering‌ problems from inhomogeneous media. We prove that these‌ special eigenvalues can be determined from full-aperture, fixed-frequency‌ far-fields using the inside-outside duality method. We then‌ show and numerically demonstrate how this method can‌ be used to reconstruct averaged values of the‌ refractive index. 2

6.3 Propagation of waves in‌ waveguides

Participants: Lucas Chesnel, Zois Moitier.‌

6.3.1 Perfect transmission in periodic waveguides with localized‌ defects

L. Chesnel, T. Creuset, Z. Moitier

In‌ this work, we study wave propagation in periodic‌ waveguides with localised defects. Generally speaking, in such‌ structures, for certain bands of frequencies, waves can‌ propagate, leading to reflection and transmission phenomena. Our goal is to identify‌ situations, by varying the‌ frequency and/or the perturbation‌‌ in the reference periodic medium, where the energy‌ of an incident wave‌ is perfectly transmitted. In‌‌ the internship of T. Creuset, we considered 1D‌ periodic materials for which‌ dispersion curves can be‌‌ computed explicitly. Then we investigated both theoretically and‌ numerically three different techniques,‌ inspired by the case‌‌ where the reference medium is homogeneous, to reach‌ perfect invisibility.

6.3.2 Eigenvalue‌ falls in thin broken‌‌ quantum strips

L. Chesnel, S.A. Nazarov

We are‌ interesting in the spectrum‌ of the Dirichlet Laplacian‌‌ in thin broken strips with angle $α$ .‌ Playing with symmetries, this‌ leads us to investigate‌‌ spectral problems for the Laplace operator with mixed‌ boundary conditions in thin‌ trapezoids characterized by a‌‌ parameter $ε$ small. We give an asymptotic expansion‌ of the first eigenvalues‌ and corresponding eigenfunctions as‌‌ $ε$ tends to zero. The new point in‌ this work is to‌ study the dependence with‌‌ respect to $α$ . We show that for‌ a small fixed $ε‌ > 0$ , at‌‌ certain particular angles ${α}_{k}^{☆}$ , $k‌ = 0, 1‌, \dots$ , that‌‌ we characterize, an eigenvalue dives, i.e. moves down‌ rapidly, below the normalized‌ threshold $π^{2} /‌‌ ε^{2}$ as $α > 0$ increases. We‌ describe the way the‌ eigenvalue dives below ${π‌‌}^{2} / ε^{2}$ and prove that the‌ phenomenon is milder at‌ $α_{0}^{☆} =‌‌ 0$ than at ${α}_{k}^{☆}$ for $k‌ \geq 1$ . 16‌

6.3.3 On the breathing‌‌ of spectral bands in periodic quantum waveguides with‌ inflating resonators

L. Chesnel,‌ S.A. Nazarov

We are‌‌ interested in the lower part of the spectrum‌ of the Dirichlet Laplacian‌ $A^{ε}$ in a‌‌ thin waveguide $Π^{ε}$ obtained by repeating periodically‌ a pattern, itself constructed‌ by scaling an inner‌‌ field geometry $Ω$ by a small factor $ε‌ > 0$ . The‌ Floquet-Bloch theory ensures that‌‌ the spectrum of ${A}^{ε}$ has a band-gap‌ structure. Due to the‌ Dirichlet boundary conditions, these‌‌ bands all move to $+ \infty$ as $O‌ (ε^{- 2‌})$ when $ε \to‌‌ 0^{+}$ . Concerning their widths, applying techniques‌ of dimension reduction, we‌ show that the results‌‌ depend on the dimension of the so-called space‌ of almost standing waves‌ in $Ω$ that we‌‌ denote by $X_{†}$ . Generically, i.e. for‌ most $Ω$ , there‌ holds $X_{†} =‌‌ {0}$ and the lower part of‌ the spectrum of ${A‌}^{ε}$ is very sparse,‌‌ made of bands of length at most $O‌ (ε)$ as‌ $ε \to 0^{+‌‌}$ . For certain $Ω$ however, we have $dim‌ X_{†} = 1‌$ and then there are‌‌ bands of length $O (1)$ which‌ allow for wave propagation‌ in $Π^{ε}$ .‌‌ The main originality of this work lies in‌ the study of the‌ behaviour of the spectral‌‌ bands when perturbing $Ω‌$ around a particular ${Ω}_{☆}$ where $\dim {X‌}_{†} = 1$ . We show a breathing‌ phenomenon for the spectrum of $A^{ε}$ :‌ when inflating $Ω$ around $Ω_{☆}$ , the‌ spectral bands rapidly expand before shrinking. In the‌ process, a band dives below the normalized threshold‌ $π^{2} / {ε}^{2}$ , stops breathing‌ and becomes extremely short as $Ω$ continues to‌ inflate. 5

6.3.4 Construction of transparent boundary conditions‌ in electromagnetic waveguides

Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel,‌ Sonia Fliss, Aurélien Parigaux

In the PhD of‌ A. Parigaux, we studied the propagation of electromagnetic‌ waves in unbounded waveguides. The objective was to‌ obtain transparent boundary conditions to bound in an‌ appropriate way the computational domain. The case of‌ heterogeneous waveguides, for which the electromagnetic coefficients vary‌ in the cross-section, raises complex issues that motivated‌ this work. In particular, determining the modes at‌ a fixed frequency leads to consider a non‌ self-adjoint problem and so-called "backward modes", for which‌ phase and group velocities have different signs, can‌ exist. In our study, we proposed and validated‌ numerically two types of transparent boundary conditions based‌ respectively on the use of an Electric-to-Magnetic (EtM)‌ operator and a Currents-to-Magnetic (CtM) operator. These allow‌ one to connect the finite element representation of‌ the approximation with a modal decomposition in the‌ unperturbed regions of the waveguide. 9

6.3.5 Trapped‌ modes in electromagnetic waveguides

Anne-Sophie Bonnet-Ben Dhia, Lucas‌ Chesnel, Sonia Fliss

We consider the Maxwell's equations‌ with perfect electric conductor boundary conditions in three-dimensional‌ unbounded domains which are the union of a‌ bounded resonator and one or several semi-infinite waveguides.‌ We are interested in the existence of electromagnetic‌ trapped modes, i.e. ${L}^{2}$ solutions of the‌ problem without source term. These trapped modes are‌ associated to eigenvalues of the Maxwell's operator, that‌ can be either below the essential spectrum or‌ embedded in it. First for homogeneous waveguides, we‌ presented different families of geometries for which we‌ can prove the existence of eigenvalues. Then we‌ exhibited certain non homogeneous waveguides with local perturbations‌ of the dielectric constants that support trapped modes.‌ Let us mention that some of the mechanisms‌ we proposed are very specific to Maxwell's equations‌ and have no equivalent for the scalar Dirichlet‌ or Neumann Laplacians. 14

6.4 Diffusion MRI

Participants:‌ J.-R. Li, A. McSweeney-Davis, S. Sedlar‌.

6.4.1 SpinDoctor-IVIM: A virtual imaging framework for‌ intravoxel incoherent motion MRI

Mojtaba Lashgari, Zheyi Yang,‌ Miguel O. Bernabeu, Jing-Rebecca Li, Alejandro F. Frangi‌

Intravoxel incoherent motion (IVIM) imaging is increasingly recognised‌ as an important tool in clinical MRI, where‌ tissue perfusion and diffusion information can aid disease‌ diagnosis, monitoring of patient recovery, and treatment outcome‌ assessment. Currently, the discovery of biomarkers based on‌ IVIM imaging, similar to other medical imaging modalities,‌ is dependent on long preclinical and clinical validation‌ pathways to link observable markers derived from images‌ with the underlying pathophysiological mechanisms. To speed up this process, virtual IVIM‌ imaging is proposed. This‌ approach provides an efficient‌‌ virtual imaging tool to design, evaluate, and optimise‌ novel approaches for IVIM‌ imaging. In this work,‌‌ virtual IVIM imaging is developed through a new‌ finite element solver, SpinDoctor-IVIM,‌ which extends SpinDoctor, a‌‌ diffusion MRI simulation toolbox. SpinDoctor-IVIM simulates IVIM imaging‌ signals by solving the‌ generalised Bloch–Torrey partial differential‌‌ equation. The input velocity to SpinDoctor-IVIM is computed‌ using HemeLB, an established‌ Lattice Boltzmann blood flow‌‌ simulator. Contrary to previous approaches, SpinDoctor-IVIM accounts for‌ volumetric microvasculature during blood‌ flow simulations, incorporates diffusion‌‌ phenomena in the intravascular space, and accounts for‌ the permeability between the‌ intravascular and extravascular spaces.‌‌ The above-mentioned features of the proposed framework are‌ illustrated with simulations on‌ a realistic microvasculature model.‌‌

6.4.2 Alpha_Mesh_Swc: automatic and robust surface mesh‌ generation from the skeleton‌ description of brain cells‌‌

Alex McSweeney-Davis, Chengran Fang, Emmanuel Caruyer, Anne Kerbrat,‌ Jing-Rebecca Li

In recent‌ years, there has been‌‌ a significant increase in publicly available skeleton descriptions‌ of real brain cells‌ from laboratories all over‌‌ the world. In theory, this should make it‌ possible to perform large‌ scale realistic simulations on‌‌ brain cells. However, currently there is still a‌ gap between the skeleton‌ descriptions and high quality‌‌ simulation-ready surface and volume meshes of brain cells.‌

We propose and implement‌ a tool called Alpha_Mesh_Swc‌‌ to generate automatically and efficiently triangular surface meshes‌ that are optimized for‌ finite elements simulations. We‌‌ use an Alpha Wrapping method with an offset‌ parameter on component surface‌ meshes to efficiently generate‌‌ a global watertight mesh. Then mesh simplification and‌ re-meshing are used to‌ produce an optimal surface‌‌ mesh. Our methodology limits the number of surface‌ triangles while preserving geometrical‌ accuracy, permits cutting and‌‌ gluing of cell components, is robust to imperfect‌ skeleton descriptions, and allows‌ mixed cell descriptions (surface‌‌ meshes combined with skeletons).

We compared the robustness,‌ performance and accuracy of‌ Alpha_Mesh_Swc against existing tools‌‌ and found significant improvement in terms of mesh‌ accuracy. We show, on‌ average, we can generate‌‌ fully automatically a brain cell (neurons or glia)‌ surface mesh in a‌ couple of minutes on‌‌ a laptop computer resulting in a simplified surface‌ mesh with only around‌ 10k nodes. The resulting‌‌ meshes were used to perform diffusion MRI simulations‌ in neurons and microglia.‌ The code and a‌‌ number of sample brain cell surface meshes have‌ been made publicly available.‌

6.5 Numerical methods and‌‌ HPC for forward problems

Participants: Antonin Boisneault,‌ Marcella Bonazzoli, Elise‌ Grosjean, Houssem Haddar‌‌, Zois Moitier, Hadrien Montanelli.

6.5.1‌ Discrete FEM-BEM coupling with‌ the Generalized Optimized Schwarz‌‌ Method

A. Boisneault, M. Bonazzoli, X. Claeys, P.‌ Marchand

We have developed‌ a non-overlapping Domain Decomposition‌‌ (DD) approach to the solution of acoustic wave‌ propagation boundary value problems‌ based on the Helmholtz‌‌ equation, on both bounded and unbounded domains. This‌ DD solver, called Generalized‌ Optimized Schwarz Method (GOSM),‌‌ is a substructuring method,‌ that is, the unknowns of an iteration are‌ associated with the subdomains interfaces. We extend the‌ existing continuous analysis to a fully discrete setting.‌ We do not consider only a specific set‌ of boundary conditions, but a whole class including,‌ e.g., Dirichlet, Neumann, and Robin conditions. Our analysis‌ also covers interface conditions corresponding to a Finite‌ Element Method - Boundary Element Method (FEM-BEM) coupling.‌ In particular, we focus on three classical FEM-BEM‌ couplings, namely the Costabel, Johnson-Nédélec and Bielak-MacCamy couplings.‌ As a remarkable outcome, the present contribution yields‌ well-posed substructured formulations of these classical FEM-BEM couplings‌ for wavenumbers different from classical spurious resonances. We‌ also establish an explicit relation between the dimensions‌ of the kernels of the initial variational formulation,‌ the local problems and the substructured formulation. This‌ relation especially holds for any wavenumber for the‌ substructured formulation of Costabel FEM-BEM coupling, which allows‌ us to prove that the latter formulation is‌ well-posed even at spurious resonances. Besides, we introduce‌ a systematically geometrically convergent iterative method for the‌ Costabel FEM-BEM coupling, with estimates on the convergence‌ speed. An article is under preparation.

6.5.2 Spurious‌ resonances for substructured FEM-BEM coupling

A. Boisneault, M.‌ Bonazzoli, X. Claeys, P. Marchand

We are interested‌ in time-harmonic acoustic scattering by an impenetrable obstacle‌ in a medium where the wavenumber is constant‌ in an exterior unbounded subdomain and is possibly‌ heterogeneous in a bounded subdomain. We consider our‌ new substructured FEM-BEM formulation, called Generalized Optimized Schwarz‌ Method (GOSM), presented in the previous subsection. Unfortunately,‌ it is well known that, even when the‌ initial boundary value problem is well-posed, the variational‌ formulation of classical FEM-BEM couplings can be ill-posed‌ for certain wavenumbers, called spurious resonances. Here, we‌ focus on the Johnson-Nédélec and Costabel couplings and‌ show that the GOSM derived from both is‌ not immune to that issue. In particular, we‌ give an explicit expression of the kernel of‌ the local operator associated with the interface between‌ the FEM and BEM subdomains. That kernel and‌ the one of classical FEM-BEM couplings are simultaneously‌ non-trivial. A proceedings paper has been submitted 12‌.

6.5.3 On the unmapped tent pitching for‌ the heterogeneous wave equation

M. Bonazzoli, G. Ciaramella,‌ I. Mazzieri

The Unmapped Tent Pitching (UTP) algorithm‌ is a space-time domain decomposition method for the‌ parallel solution of hyperbolic problems. It was originally‌ introduced for the homogeneous one-dimensional wave equation in‌ [Ciaramella, Gander, Mazzieri, 2024]. UTP is inspired by‌ the Mapped Tent Pitching (MTP) algorithm [Gopalakrishnan, Schöberl,‌ Wintersteiger, 2017], which constructs the solution by iteratively‌ building polytopal space-time subdomains, referred to as tents.‌ In MTP, each physical tent is mapped onto‌ a space-time rectangle, where local problems are solved‌ before being mapped back to the original domain.‌ In contrast, UTP avoids the nonlinear and potentially‌ singular mapping step by computing the solution directly‌ on a physical space-time rectangle that contains the‌ tent, at the expense of redundant computations in the region outside the‌ tent. In this work,‌ we investigate several strategies‌‌ to extend UTP to heterogeneous media, where the‌ wave propagation speed is‌ piecewise constant over two‌‌ subregions of the domain. Among the considered approaches,‌ the most efficient in‌ terms of computational time‌‌ is the one employing space-time subdomains with identical‌ spatial and temporal dimensions‌ in both regions, determined‌‌ by the maximum propagation speed. A proceedings paper‌ has been submitted 13‌.

6.5.4 Convergence rates‌‌ of curved boundary element methods for the 3D‌ Laplace and Helmholtz equations‌

L. Faria, P. Marchand,‌‌ H. Montanelli

We establish improved convergence rates for‌ curved boundary element methods‌ applied to the threedimensional‌‌ (3D) Laplace and Helmholtz equations with smooth geometry‌ and data. Our analysis‌ relies on a precise‌‌ analysis of the consistency errors introduced by the‌ perturbed bilinear and sesquilinear‌ forms. We illustrate our‌‌ results with numerical experiments in 3D based on‌ basis functions and curved‌ triangular elements up to‌‌ order four 17.

6.5.5 Nonlocal vector calculus‌ on the sphere

H.‌ Montanelli, M. Slevinsky, Q.‌‌ Du

We introduce a nonlocal vector calculus on‌ the unit two-sphere using‌ weakly singular integral operators.‌‌ Within this framework, the operators are diagonalizable in‌ terms of scalar and‌ vector spherical harmonics, a‌‌ property that facilitates the proof of a nonlocal‌ Stokes theorem. This constitutes‌ the first instance of‌‌ such a theorem on a curved surface. Furthermore,‌ our analysis demonstrates the‌ strong convergence of these‌‌ nonlocal operators to the classical differential operators of‌ vector calculus as the‌ interaction range tends to‌‌ zero 18.

6.5.6 High-order numerical integration on‌ self-affine sets

P. Joly,‌ M. Kachanovska, Z. Moitier‌‌

We construct an interpolatory high-order cubature rule to‌ compute integrals of smooth‌ functions over self-affine sets‌‌ with respect to an invariant measure. The main‌ difficulty is the computation‌ of the cubature weights,‌‌ which we characterize algebraically, by exploiting a self-similarity‌ property of the integral.‌ We propose an $h‌‌$ -version and a $p$ -version of the cubature,‌ present an error analysis‌ and conduct numerical experiments.‌‌

6.5.7 Cell seeding dynamics in a porous scaffold‌ material designed for meniscus‌ tissue regeneration

H. Jäger,‌‌ E. Grosjean, S. Plunder, C. Redenbach, A. Keilmann‌ , B. Simeon, C.‌ Surulescu

We study the‌‌ dynamics of a seeding experiment where a fibrous‌ scaffold material is colonized‌ by two types of‌‌ cell populations. The specific application that we have‌ in mind is related‌ to the idea of‌‌ meniscus tissue regeneration. In order to support the‌ development of a promising‌ replacement material, we discuss‌‌ certain rate equations for the densities of human‌ mesenchymal stem cells and‌ chondrocytes and for the‌‌ production of collagen-containing extracellular matrix. For qualitative studies,‌ we start with a‌ system of ordinary differential‌‌ equations and refine then the model to include‌ spatial effects of the‌ underlying nonwoven scaffold structure.‌‌ Numerical experiments as well as a complete set‌ of parameters for future‌ benchmarking are provided.

6.5.8‌‌ The non-intrusive reduced basis‌ two-grid method applied to sensitivity analysis

E. Grosjean,‌ B. Simeon

This paper deals with the derivation‌ of Non-Intrusive Reduced Basis (NIRB) techniques for sensitivity‌ analysis, more specifically the direct and adjoint state‌ methods. For highly complex parametric problems, these two‌ approaches may become too costly ans thus Reduced‌ Basis Methods (RBMs) may be a viable option.‌ We propose new NIRB two-grid algorithms for both‌ the direct and adjoint state methods in the‌ context of parabolic equations. The NIRB two-grid method‌ uses the HF code solely as a “black-box”,‌ requiring no code modification. Like other RBMs, it‌ is based on an offline-online decomposition. The offline‌ stage is time-consuming, but it is only executed‌ once, whereas the online stage employs coarser grids‌ and thus, is significantly less expensive than a‌ fine HF evaluation. On the direct method, we‌ prove on a classical model problem, the heat‌ equation, that HF evaluations of sensitivities reach an‌ optimal convergence rate in $L^{\infty} (0‌, T; {H}_{0}^{1} (Ω‌))$ , and then establish that these‌ rates are recovered by the NIRB two-grid approximation.‌ These results are supported by numerical simulations. We‌ then propose a new procedure that further reduces‌ the computational costs of the online step while‌ only computing a coarse solution of the state‌ equations. On the adjoint state method, we propose‌ a new algorithm that reduces both the state‌ and adjoint solutions. All numerical results are run‌ with the model problem as well as a‌ more complex problem, namely the Brusselator system

6.6‌ Optimization based inversion methods

Participants: Emna Abida,‌ Lorenzo Audibert, Marcella Bonazzoli, Houssem Haddar‌, Denis Vautrin.

6.6.1 Reversed one-shot inversion‌ methods

E. Abida, M. Bonazzoli, H. Haddar

We‌ are interested in the so-called one-shot methods for‌ the solution of inverse problems via gradient-based optimization‌ algorithms. The idea of the one-shot approach is‌ to couple the iterations on the state, on‌ the adjoint state and on the parameter variable.‌ In particular, the iterations on the state and‌ adjoint state are incomplete, that is, stopped before‌ achieving convergence for the associated forward and adjoint‌ problems. Hence, an inexact gradient is used to‌ update the parameter variable. Nevertheless, the convergence of‌ the coupled iterations can still be achieved. We‌ have recently performed a numerical investigation for a‌ variant where the one-shot iteration order is reversed‌ so that an actual descent direction is used‌ at each iteration. We have analyzed this reversed‌ one-shot method with one inner iteration in the‌ scalar case.

6.6.2 Imaging dam-rock interfaces in gravity‌ dams

L. Audibert, M. Bonazzoli, M. A. Boukraa,‌ H. Haddar, D. Vautrin

We are interested in‌ imaging the interface between the concrete structure of‌ a hydroelectric gravity dam and the underlying rock,‌ using Full Waveform Inversion. Indeed, it appears that‌ the roughness of the dam-rock interface has an‌ effect on the sliding stability of gravity dams. We minimize a regularized‌ misfit cost functional by‌ computing its shape derivative‌‌ and iteratively updating the interface shape by the‌ gradient descent method. Numerical‌ results using realistic noisy‌‌ synthetic data demonstrate the method ability to accurately‌ reconstruct the dam-rock interface‌ with a limited number‌‌ of measurements and in the presence of noise.‌ Moreover, the algorithm appears‌ to be robust with‌‌ respect to the heterogeneities in the concrete that‌ are typically expected in‌ the dam. An article‌‌ is under preparation.

6.6.3 Silent sources on a‌ surface for the Helmholtz‌ equation and decomposition of‌‌ $L^{2}$ vector fields

L. Bratchart, H. Haddar,‌ C.V. Guillén

We study‌ an inverse source problem‌‌ with right hand side in divergence form for‌ the Helmholtz equation, whose‌ underlying model can be‌‌ related to weak scattering from thin interfaces. This‌ inverse problem is not‌ uniquely solvable, as the‌‌ forward operator has infinite-dimensional kernel. We present a‌ decomposition of (not necessarily‌ tangent) vector fields of‌‌ $L^{2}$ -class on a closed Lipschitz surface‌ in $R^{3}$ ,‌ which allows one to‌‌ discuss an ansatz for the solution and constraints‌ that restore uniqueness. This‌ work can be seen‌‌ as a generalization of results in the literature‌ dealing with the Laplace‌ equation, but in the‌‌ Helmholtz case new ties arise between the observations‌ from each side of‌ the surface. Our proof‌‌ is based on properties of the Calderón projector‌ on the boundary of‌ Lipschitz domains, that we‌‌ establish in a ${H}^{- 1} \times {L‌}^{2}$ setting.

7 Bilateral‌ contracts and grants with‌‌ industry

7.1 Bilateral contracts with industry

Participants: Houssem‌ Haddar, Lorenzo Audibert‌.

Grant associated with‌‌ one PhD (CIFRE contract) with EDF R&D on‌ imaging with eddy current‌ using inverse problem methods.‌‌ The student is Morgan Mathevet.
Grant associated with‌ one PhD (CIFRE contract)‌ with EDF R&D on‌‌ modelling ultrasonics flow meter in heterogeneous fluid. The‌ student is Alex McSweeney-Davis.‌
Grant associated with one‌‌ PhD (CIFRE contract) with EDF R&D on imaging‌ in concrete using qualitative‌ method. The student is‌‌ Corentin Hivart

7.2 Bilateral Grants with Industry

Participants:‌ Marcella Bonazzoli, Lucas‌ Chesnel.

M. Bonazzoli‌‌ and L. Chesnel are members of ElectroMATH project‌ (Electromagnetic wave propagation in‌ complex media and configurations,‌‌ 2022-2026), granted by CIEDS (IP Paris-AID), coordinated by‌ P. Ciarlet and A.‌ Modave.

8 Partnerships and‌‌ cooperations

8.1 International initiatives

8.1.1 Associate Teams in‌ the framework of an‌ Inria International Lab or‌‌ in the framework of an Inria International Program‌

SOFIA

Participants: Lorenzo Audibert‌, Marcella Bonazzoli,‌‌ Mayeul Chavanne, Houssem Haddar.

Title:
Symbiotic‌ One-shot Forward-Inverse Algorithms
Duration:‌
2025 -> 2027
Inria‌‌ Coordinator:
Houssem Haddar
Partner Coordinator:
Slim Chaabane
Partner:‌
Faculté des Sciences de‌ Sfax, Sfax University (Tunisie)‌‌
Website:
link
Summary:
The goal of this associate‌ team is to develop‌ innovative approaches inspired by‌‌ the one-shot paradigm, which simultaneously solve the forward‌ and inverse problems in‌ a way that optimally‌‌ exploits the specificity of‌ an iterative forward solver, for instance based on‌ domain decomposition approaches for large scale problems. Our‌ aim is (i) speeding up the overall convergence‌ rate for inversion methods and (ii) efficiently addressing‌ inverse large scale (and/or time dependent) problems by‌ reducing the number of forward solves.

8.2 International‌ research visitors

8.2.1 Visits of international scientists

Other‌ international visits to the team

Slim Chaabane

Status‌
(researcher)
Institution of origin:
Faculty of Science, SFAX‌
Country:
Tunisia
Dates:
July 7-12, 2025
Context of‌ the visit:
PhD Co-advising
Mobility program/type of mobility:‌
Associate team Sofia

8.2.2 Visits to international teams‌

Sabbatical programme

Jing-Rebecca Li-Schlittgen

Visited institution:
UCLouvain (Belgique)‌
Dates of the stay:
From January 6, 2025‌ to December 31, 2025

Research stays abroad

Marcella‌ Bonazzoli

Visited institution:
MOX Laboratory, Politecnico di Milano‌
Country:
Italy
Dates:
September 2025
Context of the‌ visit:
Space-time domain decomposition methods for the heterogeneous‌ wave equation
Mobility program/type of mobility:
research stay‌

Lorenzo Audibert

Visited institution:
Departement of Mathematics, Rutgers‌ University
Country:
USA
Dates:
July-August 2025
Context of‌ the visit:
Spectral signature for anistropic media
Mobility‌ program/type of mobility:
research stay

8.3 National initiatives‌

Action exploratoire OptiGPR3D

Participants: Lorenzo Audibert, Marcella‌ Bonazzoli, Houssem Haddar, Frédéric Taillade.‌

Title:
Action exploratoire OptiGPR3D (Optimal direct and‌ inverse modeling for 3D GPR imaging in complex‌ environments)
Partner Institution(s):
IDEFIX (Inria, EDF, ENSTA‌ Paris), POEMS (CNRS, Inria, ENSTA Paris)
Duration:
Start:‌ 05/2022, 4 years
Coordinators:
Marcella Bonazzoli (IDEFIX, Inria),‌ Pierre Marchand (POEMS, Inria)
Administrator:
Inria

"Biomedical Engineering‌ Seed Grant Program" funded by the Fondation Bettencourt‌ Schueller

Participants: J.-R. Li, A. McSweeney-Davis,‌ S. Sedlar.

Title:
Investigation of potential biomarkers‌ to detect chronic inflammation in Multiple Sclerosis through‌ diffusion MRI
Partner Institution(s):
IDEFIX (Inria, EDF, ENSTA‌ Paris), CHU de Rennes, Univ Rennes
Duration:
09/2023‌ - 12/2025
Coordinators:
J.-R. Li (IDEFIX, Inria), Anne‌ Kerbrat (CHU de Rennes)
Administrator:
Inria

9 Dissemination‌

9.1 Promoting scientific activities

9.1.1 Scientific events: organisation‌

Member of the organizing committees

M. Bonazzoli (with‌ Liu-Di Lu, Tommaso Vanzan) organized a minisymposium at‌ DD29 (Milan, Italy).
M. Bonazzoli and H. Haddar‌ organized a minisymposium at PICOF 2025 (Hammamet, Tunisia).‌
Z. Moitier co-organizes the Workshop HyBOX (ENSTA, Palaiseau).‌
Z. Moitier co-organizes the minisymposium ICOSAHOM 2025 (Montréal,‌ Canada).
L. Chesnel co-organizes the seminar common to‌ the two teams IDEFIX-POEMS.

9.1.2 Scientific events: selection‌

Member of the conference program committees

L. Chesnel‌ and H. Haddar are members of the scientific‌ committee of the Waves conference at Montréal.
L.‌ Audibert (2023–) is president of the scientific committee‌ of the school CEA-EDF-Inria.
H. Haddar is member‌ of the scientific committee of the KIT Waves‌ conference (Karlsruhe) and the Picof conference (Hammamet).

9.1.3‌ Journal

Member of the editorial boards

H. Haddar‌ is member of the editorial boards of Siam‌ Journal of Mathematical Analysis and the journal Inverse‌ Problems.

Reviewer - reviewing activities

We reviewed papers‌ for international journals in the main scientific themes of the team.

9.1.4‌ Invited talks

M. Bonazzoli,‌ SIMAI 2025, biennial congress‌‌ of the Italian Society of Applied and Industrial‌ Mathematics, Trieste, Italy, Sep.‌ 2025.
M. Bonazzoli, DD29,‌‌ International Conference on Domain Decomposition Methods, Milan, Italy,‌ Jun. 2025.
M. Bonazzoli,‌ Fluid Mechanics and Waves‌‌ seminar at the New Jersey Institute of Technology,‌ United States (online), Nov.‌ 2025.
M. Bonazzoli, Seminar‌‌ in Numerical Analysis at University of Basel, Switzerland,‌ Oct. 2025.
M. Bonazzoli,‌ Seminar of Applied Mathematics‌‌ at Università di Pavia, Italy, Sep. 2025.
M.‌ Bonazzoli, Seminar at MOX‌ Laboratory, Politecnico di Milano,‌‌ Italy, Sep. 2025.
M. Bonazzoli, Seminar of the‌ Laboratoire de Mathématiques Appliquées‌ de Compiègne, France, Mar.‌‌ 2025.
L. Chesnel, conference "Wave propagation in guiding‌ structures", CIRM, Marseille, Oct.‌ 2025.
L. Chesnel gave‌‌ a course untitled "A few techniques to achieve‌ invisibility in waveguides", Summer‌ school EUR MINT 2025‌‌ - Control, Inverse Problems and Spectral Theory, Toulouse,‌ Jun. 2025. 5.5h. Corresponding‌ lecture notes 19.‌‌
Z. Moitier, Seminar LAREMA at Angers, May. 2025.‌
Z. Moitier, Seminar IDEFIX‌ at Palaiseau, April 2025.‌‌
Z. Moitier, Seminar MAC at Toulouse, Feb. 2025.‌
H. Montanelli, Inverse Problems:‌ from Foundations to Applications,‌‌ Marseille, September 2025.
H. Montanelli, Journée EDP &‌ Analyse Numérique, Inria, ENSTA‌ and École Polytechnique, Juin‌‌ 2025.
H. Haddar, Conférence WICOM, Paris, June 2025.‌
H. Haddar, Journées Onera‌ pour le CND en‌‌ aéronautique, Chatillon, June 2025.

9.1.5 Research administration

M.‌ Bonazzoli is the International‌ partnerships Scientific Correspondent for‌‌ Inria Saclay.
M. Bonazzoli took part in Mar.‌ 2025 to the prize‌ committee for SMAI-GAMNI PhD‌‌ Award 2025.
M. Bonazzoli took part in‌ Jul. 2025 to the‌ prize committee for Prix‌‌ Junior Maryam Mirzakhani awarded by Fondation Mathématique Jacques-Hadamard‌ (FMJH) to young female‌ students for a mathematics‌‌ project.
M. Bonazzoli took part in Jun. 2025‌ to the committee for‌ FMJH Care incoming mobility‌‌ scholarships offered by FMJH to enable excellent foreign‌ students with limited resources‌ to join its Bachelor's‌‌ or Master's programs in mathematics.
M. Bonazzoli is‌ a volunteer member of‌ Opération Postes (newsletter and‌‌ website, which gathers detailed information about the French‌ competitive selections for permanent‌ positions in Mathematics and‌‌ Informatics, supported by the French academic societies SMAI,‌ SAGIP, SFdS, SIF, and‌ SMF).

9.2 Teaching -‌‌ Supervision - Juries - Educational and pedagogical outreach‌

9.2.1 Teaching

Bachelor: L.‌ Chesnel, Numerical Methods for‌‌ ODEs, 3rd year of the Bachelor of Ecole‌ Polytechnique, 20 TD hours.‌
Master: L. Chesnel, Analyse‌‌ variationnelle des équations aux dérivées partielles, 2nd year‌ of Ecole Polytechnique, 40‌ TD hours.
Master: L.‌‌ Chesnel, Modal - Modélisation mathématique par la démarche‌ expérimentale, 2nd year of‌ Ecole Polytechnique, creation and‌‌ supervision of two projects for six students.
Master:‌ L. Chesnel, cosupervision of‌ a psc project of‌‌ four students, 2nd year of Ecole Polytechnique, 2h‌ meetings every 3 weeks.‌
Bachelor: M. Bonazzoli, Fonctions‌‌ de variable complexe, 1st year of Engineer School,‌ ENSTA, 12 TD hours.‌
Master: M. Bonazzoli, Calcul‌‌ scientifique parallèle, 3rd year‌ of Engineer School and 2nd year of Master,‌ ENSTA, 7 equivalent TD hours.
Lorenzo Audibert
- Bachelor:‌ Introduction to the discretization of partial differential equation‌ with finite differences, for students in the first‌ year of ENSTA curriculum. 2022-2024.
- Bachelor: Optimization, for‌ students in the first year of ENSTA curriculum.‌ 2023-.
- Bachelor: Dynamical Systems, for students in the‌ first year of ENSTA curriculum. 2025-.
Zoïs Moitier‌
- Bachelor: Fonctions d'une variable complexe, ENSTA 1A,‌ 15h (TD).
- Bachelor: Introduction aux probabilités, ENSTA‌ 1A, 15h (TD).
- Master: Eléments finis, ENSTA‌ 2A, 15h (TD/TP).
- Master: Analyse fonctionnelle, ENSTA‌ 2A, 15h (TD).
- Tutoring ENSTA student, 21h eq.‌ TD.
Hadrien Montanelli
- APM 43035 EP — Optimization‌ & Control (TA), 20h, École Polytechnique.
- APM 52009‌ EP — Machine Learning for Scientific Computing &‌ Numerical Analysis (Lecturer), 18h, École Polytechnique.
- APM 41012‌ EP — Introduction to Numerical Analysis (TA), 20h,‌ École Polytechnique 20.
Houssem Haddar
- Bachelor: Elementary‌ tools of analysis for partial differential equations, for‌ students in the first year of Ensta curriculum.‌ 28 equivalent TD hours.
- Bachelor: Optimization quadratique. Lecture‌ course (for the entire cohort and tutori- als‌ for first-year students in the ENSTA curriculum. 24‌ equivalent TD hours.

9.2.2 Supervision

Master internship: E.‌ Abida, Analysis of a new variant of the‌ one-shot methods for inverse problems, (Apr–Sep. 2025), M.‌ Bonazzoli and H. Haddar.
Master internship: T. Creuset,‌ Perfect transmission in periodic waveguides with localized defects,‌ (Apr–Sep. 2025), L. Chesnel and Z. Moitier.
PhD‌ in progress: A. Boisneault, Numerical methods and high‌ performance simulation for 3D imaging in complex media,‌ (2023-), M. Bonazzoli (with X. Claeys, ENSTA, and‌ P. Marchand, Inria).
PhD in progress: C. Hivart,‌ Sampling Methods for concrete like material, (2024-), L.‌ Audibert and H. Haddar
PhD in progress: A.‌ McSweeney-Davis, Modelling of wave propagation in heterogeneous moving‌ fluid, (2024-), L. Audibert and H. Haddar
PhD‌ in progress: M. Chavanne, Spectral Signature for Maxwell‌ equations, (2024-), L. Audibert and H. Haddar
PhD‌ in progress: A. Boisneault, Numerical methods and high‌ performance simulation for 3D imaging in complex media,‌ (2023-), M. Bonazzoli (with X. Claeys, ENSTA, and‌ P. Marchand, Inria).
PhD defended (17/12/2025): A. Parigaux,‌ Construction of transparent conditions for electromagnetic waveguides, analysis‌ and applications, L. Chesnel (with A.-S. Bonnet-BenDhia and‌ S. Fliss, Poems).
PhD defended (10/10/2025): M. Mathevet,‌ Imagerie par courant de Foucault des fissures et‌ dépôts dans les GV par méthodes inverses, analysis‌ and applications, L. Audibert and H. Haddar.
Postdoc:‌ A. Rappaport, Domain decomposition methods for electromagnetic waves‌ in anisotropic complex media, (2025-), M. Bonazzoli (with‌ P. Ciarlet, ENSTA, and A. Modave, CNRS).
Postdoc:‌ M. Zaccaron, Invisibility in electromagnetic waveguides, (01/09/2025-), L.‌ Chesnel.
PhD in progress: V. Chenu, SiML applied‌ to linear sampling methods (2024-). H. Motanelli and‌ H. Haddar.
PhD in progress: E. Jung, Curved‌ boundary elements for elasticity scattering problems (2025-). H.‌ Motanelli and H. Haddar.
PhD in progress: C.‌ Regaig, Kohn-Vogelius approach for non symmetric inverse problems (2024-). S. Chaabane and‌ H. Haddar.

9.2.3 Juries‌

M. Bonazzoli took part‌‌ in Apr.–May 2025 in the recruitment committee (‌comité de sélection)‌ for the 2025 recruitment‌‌ campaign of an Associate professor (Maître de conférences)‌ at Université de Lorraine.‌
M. Bonazzoli took part‌‌ in the PhD thesis defense committee of Charlotte‌ Milano (University of Reims‌ Champagne-Ardenne).

9.2.4 Participation in‌‌ Live events

M. Bonazzoli participated to speed-meetings with‌ female high school students‌ (Rendez-vous des Jeunes Mathématiciennes‌‌ et Informaticiennes at Inria Saclay, Oct. 2025), to‌ answer their questions about‌ the studies and career‌‌ as a mathematician.
L. Chesnel was volunteer at‌ Inria stand at Fête‌ de la Science (Institut‌‌ Polytechnique de Paris), Oct. 2025.

10 Scientific production‌

10.1 Major publications

1‌ miscA.-S.Anne-Sophie Bonnet-Ben‌‌ Dhia, L.Lucas Chesnel and S.Sonia‌ Fliss. Trapped modes‌ in electromagnetic waveguides.‌‌December 2025HAL

10.2 Publications of the year‌

International journals

2 article‌L.Lorenzo Audibert,‌‌ H.Houssem Haddar and F.Fabien Pourre.‌ Averaged Steklov Eigenvalues, Inside‌ Outside Duality and Application‌‌ to Inverse Scattering.SIAM Journal on Applied‌ Mathematics2025. In‌ press. HAL back to‌‌ text
3 articleA.-S.Anne-Sophie Bonnet-Ben Dhia,‌ L.Lucas Chesnel and‌ M.Mahran Rihani.‌‌ Maxwell's equations with hypersingularities at a negative index‌ material conical tip.‌Pure and Applied Analysis‌‌712025, 127–169HAL
4 article‌L.Lucas Chesnel,‌ H.Houssem Haddar,‌‌ H.Hongjie Li and J.Jingni Xiao.‌ Examples of non-scattering inhomogeneities‌.Inverse Problems and‌‌ Imaging 195October 2025HAL back to‌ text
5 articleL.‌Lucas Chesnel and S.‌‌ A.Sergei A Nazarov. On the breathing‌ of spectral bands in‌ periodic quantum waveguides with‌‌ inflating resonators.ESAIM: Mathematical Modelling and Numerical‌ Analysis5942025‌HAL back to text‌‌
6 articleE.Elise Grosjean and B.Bernd‌ Simeon. The non-intrusive‌ reduced basis two-grid method‌‌ applied to sensitivity analysis.ESAIM: Mathematical Modelling‌ and Numerical Analysis59‌1January 2025,‌‌ 101-135HAL DOI
7 articleH.Houssem Haddar‌ and N.Nouha Jenhani‌. Analysis of the‌‌ interior transmission problem in an unbounded locally perturbed‌ periodic strip.Inverse‌ Problems and Imaging 20‌‌2025, 305-329In press. HAL DOI back‌ to text
8 article‌A.Alex Mcsweeney-Davis,‌‌ C.Chengran Fang, E.Emmanuel Caruyer,‌ A.Anne Kerbrat and‌ J.-R.Jing-Rebecca Li.‌‌ Alpha Mesh Swc: automatic and robust surface mesh‌ generation from the skeleton‌ description of brain cells‌‌.Briefings in Bioinformatics263January 2025‌HAL DOI

International peer-reviewed‌ conferences

9 inproceedingsA.-S.‌‌Anne-Sophie Bonnet-Ben Dhia, L.Lucas Chesnel,‌ S.Sonia Fliss and‌ A.Aurélien Parigaux.‌‌ Mathematical and numerical analysis of the modes of‌ a heterogeneous electromagnetic waveguide.‌.WAVES 2025 -‌‌ Conference on Mathematics of Wave PhenomenaKarlsruhe, Germany‌February 2025HAL back‌ to text

Conferences without‌‌ proceedings

10 inproceedingsM.‌Mohamed Belmokhtar, N.Nabil Maifia, G.‌Géraldine Villain, D.Denis Vautrin and A.‌Alexis Cothenet. Approaches and limitations of Non-Destructive‌ Testing for evaluating bituminous concrete using wave propagation:‌ A review from the laboratory test to in‌ situ case study.International Symposium on Nondestructive‌ Testing in Civil Engineering (NDT-CE 2025)3010‌IZMIR, TurkeyOctober 2025HAL DOI
11 inproceedings‌N.Nabil Maifia, M.Mohamed Belmokhtar,‌ G.Géraldine Villain, D.Denis Vautrin,‌ F.Frédéric Taillade and A.Alexis Cothenet.‌ Non-Destructive Ultrasonic Evaluation of Asphalt Concrete Waterproofing in‌ Hydraulic Structures: Experimental and Numerical Study.International‌ Symposium on Nondestructive Testing in Civil Engineering (NDT-CE‌ 2025)3010IZMIR, TurkeyOctober 2025HAL‌DOI

Reports & preprints

12 miscA.Antonin‌ Boisneault, M.Marcella Bonazzoli, X.Xavier‌ Claeys and P.Pierre Marchand. Spurious resonances‌ for substructured FEM-BEM coupling.November 2025HAL‌back to text
13 miscM.Marcella Bonazzoli‌, G.Gabriele Ciaramella and I.Ilario Mazzieri‌. On the unmapped tent pitching for the‌ heterogeneous wave equation.December 2025HAL back‌ to text
14 miscA.-S.Anne-Sophie Bonnet-Ben Dhia‌, L.Lucas Chesnel and S.Sonia Fliss‌. Trapped modes in electromagnetic waveguides.December‌ 2025HAL back to text
15 miscD.-Q.‌Duc-Quang Bui, B.Bérangère Delourme, L.‌Laurence Halpern and F.Felix Kwok. Optimized‌ Schwarz Methods in Time for Discrete Transport Control‌.June 2025HAL
16 miscL.Lucas‌ Chesnel and S. A.Sergei A. Nazarov.‌ Eigenvalue falls in thin broken quantum strips.‌August 2025HAL back to text
17 misc‌L.Luiz Faria, P.Pierre Marchand and‌ H.Hadrien Montanelli. Convergence rates of curved‌ boundary element methods for the 3D Laplace and‌ Helmholtz equations.July 2025HAL back to‌ text
18 miscH.Hadrien Montanelli, R.‌ M.Richard Mikael Slevinsky and Q.Qiang Du‌. Nonlocal vector calculus on the sphere.‌2025HAL DOI back to text

Educational activities‌

19 unpublishedL.Lucas Chesnel. A few‌ techniques to achieve invisibility in waveguides.June‌ 2025, DoctoralFranceHAL back to text‌
20 unpublishedH.Hadrien Montanelli. Machine Learning‌ for Scientific Computing and Numerical Analysis.January‌ 2025, MasterFranceHAL back to text‌

IDEFIX - 2025

IDEFIX - 2025

2025﻿​﻿﻿Activity reportProject-TeamIDEFIX​‌﻿﻿

Keywords

Computer﻿​﻿﻿ Science and Digital Science​‌﻿﻿

Other​​﻿﻿ Research Topics and Application​​​‌ Domains

1﻿​﻿﻿ Team members, visitors, external​‌﻿﻿ collaborators

Research Scientists

Faculty​​​‌ Members

Post-Doctoral Fellows

PhD Students

Technical Staff﻿‌​‌

Interns﻿﻿﻿‌ and Apprentices

Administrative Assistant

Visiting﻿﻿﻿‌ Scientists

External Collaborators﻿﻿﻿‌

2 Overall objectives

3 Research program

4 Application​​﻿﻿ domains

4.1 Eddy Current​​​‌ Imaging for steam generator﻿​﻿﻿ and rotating machine

4.2 Non destructive testing﻿﻿﻿‌ of concrete-like material

4.3 Subsurface imaging​​​‌

4.4 Applications of​​​‌ concepts related to invisibility﻿​﻿﻿ for finite set of​‌﻿﻿ measurements

4.5 Other​​​‌ potential applications of interest﻿﻿﻿‌ for EDF

4.6 Diffusion MRI

5 Latest​​​‌ software developments, platforms, open﻿​﻿﻿ data

5.1 Latest software​‌﻿﻿ developments

5.1.1 ECIP

5.1.2﻿​﻿﻿ SpinDoctor

5.1.3 CASTOR

5.1.4 lostinmsh﻿​​﻿

5.1.5 HAdaptiveIntegration.jl

5.1.6 Reduced Basis​​​‌ Methods Documentation

6 New results﻿﻿﻿‌

6.1 Fast data driven﻿‌​‌ imaging methods

6.1.1 Analysis﻿​​﻿ of Sampling methods with​​​‌ and without linearization

6.1.2 Fast﻿‌​‌ Imaging of Local Perturbations﻿​​﻿ in a Unknown Bi-Periodic​​​‌ Layered Medium

6.2 Transmission​​​‌ eigenvalues

6.2.1​​﻿﻿ Examples of non-scattering inhomogeneities​​​‌

6.2.2 Averaged Steklov Eigenvalues,﻿​﻿﻿ Inside OutsideDuality and Application​‌﻿﻿ to Inverse Scattering

6.3﻿​﻿﻿ Propagation of waves in​‌﻿﻿ waveguides

6.3.1 Perfect transmission in﻿​﻿﻿ periodic waveguides with localized​‌﻿﻿ defects

6.3.2 Eigenvalue﻿﻿﻿‌ falls in thin broken﻿‌​‌ quantum strips

6.3.3 On the breathing﻿‌​‌ of spectral bands in﻿​​﻿ periodic quantum waveguides with​​​‌ inflating resonators

6.3.4 Construction﻿​﻿﻿ of transparent boundary conditions​‌﻿﻿ in electromagnetic waveguides

6.3.5 Trapped​​​‌ modes in electromagnetic waveguides﻿​﻿﻿

6.4 Diffusion MRI

6.4.1 SpinDoctor-IVIM: A﻿​﻿﻿ virtual imaging framework for​‌﻿﻿ intravoxel incoherent motion MRI​​﻿﻿

6.4.2 Alpha_Mesh_Swc: automatic﻿​​﻿ and robust surface mesh​​​‌ generation from the skeleton﻿﻿﻿‌ description of brain cells﻿‌​‌

6.5 Numerical methods and﻿‌​‌ HPC for forward problems﻿​​﻿

6.5.1​​​‌ Discrete FEM-BEM coupling with﻿﻿﻿‌ the Generalized Optimized Schwarz﻿‌​‌ Method

6.5.2 Spurious​‌﻿﻿ resonances for substructured FEM-BEM​​﻿﻿ coupling

6.5.3 On the​​﻿﻿ unmapped tent pitching for​​​‌ the heterogeneous wave equation﻿​﻿﻿

6.5.4 Convergence rates﻿‌​‌ of curved boundary element﻿​​﻿ methods for the 3D​​​‌ Laplace and Helmholtz equations﻿﻿﻿‌

6.5.5 Nonlocal vector calculus​​​‌ on the sphere

6.5.6﻿​​﻿ High-order numerical integration on​​​‌ self-affine sets

6.5.7 Cell seeding dynamics﻿​​﻿ in a porous scaffold​​​‌ material designed for meniscus﻿﻿﻿‌ tissue regeneration

6.5.8﻿‌​‌ The non-intrusive reduced basis​​​‌ two-grid method applied to﻿​﻿﻿ sensitivity analysis

6.6​​​‌ Optimization based inversion methods﻿​﻿﻿

6.6.1 Reversed one-shot inversion​‌﻿﻿ methods

6.6.2 Imaging﻿​﻿﻿ dam-rock interfaces in gravity​‌﻿﻿ dams

6.6.3﻿​​﻿ Silent sources on a​​​‌ surface for the Helmholtz﻿﻿﻿‌ equation and decomposition of﻿‌​‌ L2 vector fields﻿​​﻿

7 Bilateral﻿﻿﻿‌ contracts and grants with﻿‌​‌ industry

7.1 Bilateral contracts﻿​​﻿ with industry

7.2 Bilateral﻿​​﻿ Grants with Industry

8 Partnerships and﻿‌​‌ cooperations

8.1 International initiatives﻿​​﻿

8.1.1 Associate Teams in​​​‌ the framework of an﻿﻿﻿‌ Inria International Lab or﻿‌​‌ in the framework of﻿​​﻿ an Inria International Program​​​‌

SOFIA

8.2 International​​​‌ research visitors

8.2.1 Visits﻿​﻿﻿ of international scientists

Other​‌﻿﻿ international visits to the​​﻿﻿ team

Slim Chaabane

8.2.2​​﻿﻿ Visits to international teams​​​‌

Sabbatical programme

Jing-Rebecca Li-Schlittgen﻿​﻿﻿

Research stays abroad

Marcella​‌﻿﻿ Bonazzoli

Lorenzo Audibert

8.3 National initiatives​‌﻿﻿

2025Activity reportProject-TeamIDEFIX‌

Computer Science and Digital Science‌

Other Research Topics and Application‌ Domains

1 Team members, visitors, external‌ collaborators

Faculty‌ Members

Technical Staff‌‌

Interns‌ and Apprentices

Visiting‌ Scientists

External Collaborators‌

4 Application domains

4.1 Eddy Current‌ Imaging for steam generator and rotating machine

4.2 Non destructive testing‌ of concrete-like material

4.3 Subsurface imaging‌

4.4 Applications of‌ concepts related to invisibility for finite set of‌ measurements

4.5 Other‌ potential applications of interest‌ for EDF

5 Latest‌ software developments, platforms, open data

5.1 Latest software‌ developments

5.1.2 SpinDoctor

5.1.4 lostinmsh

5.1.6 Reduced Basis‌ Methods Documentation

6 New results‌

6.1 Fast data driven‌‌ imaging methods

6.1.1 Analysis of Sampling methods with‌ and without linearization

6.1.2 Fast‌‌ Imaging of Local Perturbations in a Unknown Bi-Periodic‌ Layered Medium

6.2 Transmission‌ eigenvalues

6.2.1 Examples of non-scattering inhomogeneities‌

6.2.2 Averaged Steklov Eigenvalues, Inside OutsideDuality and Application‌ to Inverse Scattering

6.3 Propagation of waves in‌ waveguides

6.3.1 Perfect transmission in periodic waveguides with localized‌ defects

6.3.2 Eigenvalue‌ falls in thin broken‌‌ quantum strips

6.3.3 On the breathing‌‌ of spectral bands in periodic quantum waveguides with‌ inflating resonators

6.3.4 Construction of transparent boundary conditions‌ in electromagnetic waveguides

6.3.5 Trapped‌ modes in electromagnetic waveguides

6.4.1 SpinDoctor-IVIM: A virtual imaging framework for‌ intravoxel incoherent motion MRI

6.4.2 Alpha_Mesh_Swc: automatic and robust surface mesh‌ generation from the skeleton‌ description of brain cells‌‌

6.5 Numerical methods and‌‌ HPC for forward problems

6.5.1‌ Discrete FEM-BEM coupling with‌ the Generalized Optimized Schwarz‌‌ Method

6.5.2 Spurious‌ resonances for substructured FEM-BEM coupling

6.5.3 On the unmapped tent pitching for‌ the heterogeneous wave equation

6.5.4 Convergence rates‌‌ of curved boundary element methods for the 3D‌ Laplace and Helmholtz equations‌

6.5.5 Nonlocal vector calculus‌ on the sphere

6.5.6 High-order numerical integration on‌ self-affine sets

6.5.7 Cell seeding dynamics in a porous scaffold‌ material designed for meniscus‌ tissue regeneration

6.5.8‌‌ The non-intrusive reduced basis‌ two-grid method applied to sensitivity analysis

6.6‌ Optimization based inversion methods

6.6.1 Reversed one-shot inversion‌ methods

6.6.2 Imaging dam-rock interfaces in gravity‌ dams

6.6.3 Silent sources on a‌ surface for the Helmholtz‌ equation and decomposition of‌‌ $L^{2}$ vector fields

7 Bilateral‌ contracts and grants with‌‌ industry

7.1 Bilateral contracts with industry

7.2 Bilateral Grants with Industry

8 Partnerships and‌‌ cooperations

8.1 International initiatives

8.1.1 Associate Teams in‌ the framework of an‌ Inria International Lab or‌‌ in the framework of an Inria International Program‌

8.2 International‌ research visitors

8.2.1 Visits of international scientists

Other‌ international visits to the team

8.2.2 Visits to international teams‌

Jing-Rebecca Li-Schlittgen

Marcella‌ Bonazzoli

8.3 National initiatives‌

"Biomedical Engineering‌ Seed Grant Program" funded by the Fondation Bettencourt‌ Schueller

9 Dissemination‌

9.1 Promoting scientific activities

9.1.1 Scientific events: organisation‌

Member of the organizing committees

9.1.2 Scientific events: selection‌

Member of the conference program committees

9.1.3‌ Journal

Member of the editorial boards

Reviewer - reviewing activities

9.1.4‌ Invited talks

9.2 Teaching -‌‌ Supervision - Juries - Educational and pedagogical outreach‌

9.2.2 Supervision

9.2.3 Juries‌

9.2.4 Participation in‌‌ Live events

10 Scientific production‌

10.2 Publications of the year‌

International peer-reviewed‌ conferences

Conferences without‌‌ proceedings